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How do you calculate the magnitude of vectors?

Answer 1

A ruler can be used to measure the vector's magnitude if an accurately drawn scaled vector diagram is utilized.

For instance:

What is the displacement of a car that moves 120 km east, then turns north and moves another 50 km?

This could be drawn using carefully drawn vectors, drawn to an appropriate scale such as 1 cm = 20 km. This would mean drawing a 6.0 cm arrow, pointing east, then a 2.5 cm arrow drawn head-to-tail, pointing north (#90^o# angle between). The displacement is the straight-line, "as the crow flies" distance between the starting point and the ending point, which should work out to a 6.5 cm long arrow pointing approximately #23^o# north of east.

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Answer 2

Emily Abbate

To calculate the magnitude of a vector, you use the formula:

[ |\vec{v}| = \sqrt{v_1^2 + v_2^2 + \ldots + v_n^2} ]

where ( \vec{v} ) is the vector with components ( v_1, v_2, \ldots, v_n ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.